State Treasurer Steve Grossman on Wednesday pushed Democratic gubernatorial campaign rival Attorney General Martha Coakley to abide by a campaign finance pact designed to limit third-party spending.

Grossman, whom Coakley joined as the best-known Democrat in the primary field, issued a press release calling on her to sign a modified version of “the People’s Pledge,” an agreement that has become commonplace in Massachusetts campaigns. Under the pledge, if a third-party group pays for ads or mail in support of one candidate, that candidate must make a charitable contribution of equal amount.

Grossman’s proposal calls for the money to go to The One Fund, organized in the wake of the Boston Marathon bombings to support victims.

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In response, Coakley’s campaign released a statement saying she would pursue some type of pledge, although not necessarily the one proposed by Grossman.

“I applaud the leadership that Elizabeth Warren and Scott Brown showed in signing the original ‘people’s pledge’ and look forward to working with other candidates in this race to put in place a similar agreement,” Coakley said in the statement. “My campaign will work with the other Democratic candidates to finalize a people’s pledge for the primary.”

The pledge became popular during the 2012 US Senate campaign between Elizabeth Warren and Scott Brown, when both candidates agreed to sign it as a way to limit outside spending in one of the nation’s most closely watched races that year.

In a nod to the crowded Democratic primary, Grossman’s proposal also calls for contributions to be made by candidates if they have been “expressly supported” by an organization that subsequently pays for campaign media in opposition to another candidate.

The other candidates in the Democratic primary are Donald M. Berwick, a former director of the federal Medicaid program; Juliette N. Kayyem, a former Globe columnist and onetime state and federal homeland security official; and Joseph C. Avellone, a biotechnology executive. State Senator Daniel A. Wolf has suspended his campaign while trying to resolve ethics questions stemming from his ownership stake in Cape Air.